.. currentmodule:: numpy

.. _arrays.dtypes:

**********************************
Data type objects (:class:`dtype`)
**********************************

A data type object (an instance of :class:`numpy.dtype` class)
describes how the bytes in the fixed-size block of memory
corresponding to an array item should be interpreted. It describes the
following aspects of the data:

1. Type of the data (integer, float, Python object, etc.)
2. Size of the data (how many bytes is in *e.g.* the integer)
3. Byte order of the data (:term:`little-endian` or :term:`big-endian`)
4. If the data type is a :term:`record`, an aggregate of other
   data types, (*e.g.*, describing an array item consisting of
   an integer and a float),

   1. what are the names of the ":term:`fields <field>`" of the record,
      by which they can be :ref:`accessed <arrays.indexing.rec>`,
   2. what is the data-type of each :term:`field`, and
   3. which part of the memory block each field takes.

5. If the data is a sub-array, what is its shape and data type.

.. index::
   pair: dtype; scalar

To describe the type of scalar data, there are several :ref:`built-in
scalar types <arrays.scalars.built-in>` in Numpy for various precision
of integers, floating-point numbers, *etc*. An item extracted from an
array, *e.g.*, by indexing, will be a Python object whose type is the
scalar type associated with the data type of the array.

Note that the scalar types are not :class:`dtype` objects, even though
they can be used in place of one whenever a data type specification is
needed in Numpy.

.. index::
   pair: dtype; field
   pair: dtype; record

Record data types are formed by creating a data type whose
:term:`fields` contain other data types. Each field has a name by
which it can be :ref:`accessed <arrays.indexing.rec>`. The parent data
type should be of sufficient size to contain all its fields; the
parent can for example be based on the :class:`void` type which allows
an arbitrary item size. Record data types may also contain other record
types and fixed-size sub-array data types in their fields.

.. index::
   pair: dtype; sub-array

Finally, a data type can describe items that are themselves arrays of
items of another data type. These sub-arrays must, however, be of a
fixed size. If an array is created using a data-type describing a
sub-array, the dimensions of the sub-array are appended to the shape
of the array when the array is created. Sub-arrays in a field of a
record behave differently, see :ref:`arrays.indexing.rec`.

.. admonition:: Example

   A simple data type containing a 32-bit big-endian integer:
   (see :ref:`arrays.dtypes.constructing` for details on construction)

   >>> dt = np.dtype('>i4')
   >>> dt.byteorder
   '>'
   >>> dt.itemsize
   4
   >>> dt.name
   'int32'
   >>> dt.type is np.int32
   True

   The corresponding array scalar type is :class:`int32`.

.. admonition:: Example

   A record data type containing a 16-character string (in field 'name')
   and a sub-array of two 64-bit floating-point number (in field 'grades'):

   >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))])
   >>> dt['name']
   dtype('|S16')
   >>> dt['grades']
   dtype(('float64',(2,)))

   Items of an array of this data type are wrapped in an :ref:`array
   scalar <arrays.scalars>` type that also has two fields:

   >>> x = np.array([('Sarah', (8.0, 7.0)), ('John', (6.0, 7.0))], dtype=dt)
   >>> x[1]
   ('John', [6.0, 7.0])
   >>> x[1]['grades']
   array([ 6.,  7.])
   >>> type(x[1])
   <type 'numpy.void'>
   >>> type(x[1]['grades'])
   <type 'numpy.ndarray'>

.. _arrays.dtypes.constructing:

Specifying and constructing data types
======================================

Whenever a data-type is required in a NumPy function or method, either
a :class:`dtype` object or something that can be converted to one can
be supplied.  Such conversions are done by the :class:`dtype`
constructor:

.. autosummary::
   :toctree: generated/

   dtype

What can be converted to a data-type object is described below:

:class:`dtype` object

   .. index::
      triple: dtype; construction; from dtype

   Used as-is.

:const:`None`

   .. index::
      triple: dtype; construction; from None

   The default data type: :class:`float_`.

.. index::
   triple: dtype; construction; from type

Array-scalar types

    The 21 built-in :ref:`array scalar type objects
    <arrays.scalars.built-in>` all convert to an associated data-type object.
    This is true for their sub-classes as well.

    Note that not all data-type information can be supplied with a
    type-object: for example, :term:`flexible` data-types have
    a default *itemsize* of 0, and require an explicitly given size
    to be useful.

    .. admonition:: Example

       >>> dt = np.dtype(np.int32)       # 32-bit integer
       >>> dt = np.dtype(np.complex128)  # 128-bit complex floating-point number

Generic types

    The generic hierarchical type objects convert to corresponding
    type objects according to the associations:

    =====================================================  ===============
    :class:`number`, :class:`inexact`, :class:`floating`   :class:`float`
    :class:`complexfloating`                               :class:`cfloat`
    :class:`integer`, :class:`signedinteger`               :class:`int\_`
    :class:`unsignedinteger`                               :class:`uint`
    :class:`character`                                     :class:`string`
    :class:`generic`, :class:`flexible`                    :class:`void`
    =====================================================  ===============

Built-in Python types

    Several python types are equivalent to a corresponding
    array scalar when used to generate a :class:`dtype` object:

    ================  ===============
    :class:`int`      :class:`int\_`
    :class:`bool`     :class:`bool\_`
    :class:`float`    :class:`float\_`
    :class:`complex`  :class:`cfloat`
    :class:`str`      :class:`string`
    :class:`unicode`  :class:`unicode\_`
    :class:`buffer`   :class:`void`
    (all others)      :class:`object_`
    ================  ===============

    .. admonition:: Example

       >>> dt = np.dtype(float)   # Python-compatible floating-point number
       >>> dt = np.dtype(int)     # Python-compatible integer
       >>> dt = np.dtype(object)  # Python object

Types with ``.dtype``

    Any type object with a ``dtype`` attribute: The attribute will be
    accessed and used directly. The attribute must return something
    that is convertible into a dtype object.

.. index::
   triple: dtype; construction; from string

Several kinds of strings can be converted. Recognized strings can be
prepended with ``'>'`` (:term:`big-endian`), ``'<'``
(:term:`little-endian`), or ``'='`` (hardware-native, the default), to
specify the byte order.

One-character strings

    Each built-in data-type has a character code
    (the updated Numeric typecodes), that uniquely identifies it.

    .. admonition:: Example

       >>> dt = np.dtype('b')  # byte, native byte order
       >>> dt = np.dtype('>H') # big-endian unsigned short
       >>> dt = np.dtype('<f') # little-endian single-precision float
       >>> dt = np.dtype('d')  # double-precision floating-point number

Array-protocol type strings (see :ref:`arrays.interface`)

   The first character specifies the kind of data and the remaining
   characters specify how many bytes of data. The supported kinds are

   ================   ========================
   ``'b'``            Boolean
   ``'i'``            (signed) integer
   ``'u'``            unsigned integer
   ``'f'``            floating-point
   ``'c'``            complex-floating point
   ``'S'``, ``'a'``   string
   ``'U'``            unicode
   ``'V'``            anything (:class:`void`)
   ================   ========================

   .. admonition:: Example

      >>> dt = np.dtype('i4')   # 32-bit signed integer
      >>> dt = np.dtype('f8')   # 64-bit floating-point number
      >>> dt = np.dtype('c16')  # 128-bit complex floating-point number
      >>> dt = np.dtype('a25')  # 25-character string

String with comma-separated fields

   Numarray introduced a short-hand notation for specifying the format
   of a record as a comma-separated string of basic formats.

   A basic format in this context is an optional shape specifier
   followed by an array-protocol type string. Parenthesis are required
   on the shape if it is greater than 1-d. NumPy allows a modification
   on the format in that any string that can uniquely identify the
   type can be used to specify the data-type in a field.
   The generated data-type fields are named ``'f0'``, ``'f2'``, ...,
   ``'f<N-1>'`` where N (>1) is the number of comma-separated basic
   formats in the string. If the optional shape specifier is provided,
   then the data-type for the corresponding field describes a sub-array.

   .. admonition:: Example

      - field named ``f0`` containing a 32-bit integer
      - field named ``f1`` containing a 2 x 3 sub-array
        of 64-bit floating-point numbers
      - field named ``f2`` containing a 32-bit floating-point number

      >>> dt = np.dtype("i4, (2,3)f8, f4")

      - field named ``f0`` containing a 3-character string
      - field named ``f1`` containing a sub-array of shape (3,)
        containing 64-bit unsigned integers
      - field named ``f2`` containing a 3 x 4 sub-array
        containing 10-character strings

      >>> dt = np.dtype("a3, 3u8, (3,4)a10")

Type strings

   Any string in :obj:`numpy.sctypeDict`.keys():

   .. admonition:: Example

      >>> dt = np.dtype('uint32')   # 32-bit unsigned integer
      >>> dt = np.dtype('Float64')  # 64-bit floating-point number

.. index::
   triple: dtype; construction; from tuple

``(flexible_dtype, itemsize)``

    The first argument must be an object that is converted to a
    flexible data-type object (one whose element size is 0), the
    second argument is an integer providing the desired itemsize.

    .. admonition:: Example

       >>> dt = np.dtype((void, 10))  # 10-byte wide data block
       >>> dt = np.dtype((str, 35))   # 35-character string
       >>> dt = np.dtype(('U', 10))   # 10-character unicode string

``(fixed_dtype, shape)``

    .. index::
       pair: dtype; sub-array

    The first argument is any object that can be converted into a
    fixed-size data-type object. The second argument is the desired
    shape of this type. If the shape parameter is 1, then the
    data-type object is equivalent to fixed dtype. If *shape* is a
    tuple, then the new dtype defines a sub-array of the given shape.

    .. admonition:: Example

       >>> dt = np.dtype((np.int32, (2,2)))            # 2 x 2 integer sub-array
       >>> dt = np.dtype(('S10', 1))                   # 10-character string
       >>> dt = np.dtype(('i4, (2,3)f8, f4', (2,3)))   # 2 x 3 record sub-array

``(base_dtype, new_dtype)``

    Both arguments must be convertible to data-type objects in this
    case. The *base_dtype* is the data-type object that the new
    data-type builds on. This is how you could assign named fields to
    any built-in data-type object.

    .. admonition:: Example

       32-bit integer, whose first two bytes are interpreted as an integer
       via field ``real``, and the following two bytes via field ``imag``.

       >>> dt = np.dtype((np.int32, {'real': (np.int16, 0), 'imag': (np.int16, 2)})

       32-bit integer, which is interpreted as consisting of a sub-array
       of shape ``(4,)`` containing 8-bit integers:

       >>> dt = np.dtype((np.int32, (np.int8, 4)))

       32-bit integer, containing fields ``r``, ``g``, ``b``, ``a`` that
       interpret the 4 bytes in the integer as four unsigned integers:

       >>> dt = np.dtype(('i4', [('r','u1'),('g','u1'),('b','u1'),('a','u1')]))

.. note:: XXX: does the second-to-last example above make sense?

.. index::
   triple: dtype; construction; from list

``[(field_name, field_dtype, field_shape), ...]``

   *obj* should be a list of fields where each field is described by a
   tuple of length 2 or 3. (Equivalent to the ``descr`` item in the
   :obj:`__array_interface__` attribute.)

   The first element, *field_name*, is the field name (if this is
   ``''`` then a standard field name, ``'f#'``, is assigned).  The
   field name may also be a 2-tuple of strings where the first string
   is either a "title" (which may be any string or unicode string) or
   meta-data for the field which can be any object, and the second
   string is the "name" which must be a valid Python identifier.

   The second element, *field_dtype*, can be anything that can be
   interpreted as a data-type.

   The optional third element *field_shape* contains the shape if this
   field represents an array of the data-type in the second
   element. Note that a 3-tuple with a third argument equal to 1 is
   equivalent to a 2-tuple.

   This style does not accept *align* in the :class:`dtype`
   constructor as it is assumed that all of the memory is accounted
   for by the array interface description.

   .. admonition:: Example

      Data-type with fields ``big`` (big-endian 32-bit integer) and
      ``little`` (little-endian 32-bit integer):

      >>> dt = np.dtype([('big', '>i4'), ('little', '<i4')])

      Data-type with fields ``R``, ``G``, ``B``, ``A``, each being an
      unsigned 8-bit integer:

      >>> dt = np.dtype([('R','u1'), ('G','u1'), ('B','u1'), ('A','u1')])

.. index::
   triple: dtype; construction; from dict

``{'names': ..., 'formats': ..., 'offsets': ..., 'titles': ...}``

    This style has two required and two optional keys.  The *names*
    and *formats* keys are required. Their respective values are
    equal-length lists with the field names and the field formats.
    The field names must be strings and the field formats can be any
    object accepted by :class:`dtype` constructor.

    The optional keys in the dictionary are *offsets* and *titles* and
    their values must each be lists of the same length as the *names*
    and *formats* lists. The *offsets* value is a list of byte offsets
    (integers) for each field, while the *titles* value is a list of
    titles for each field (:const:`None` can be used if no title is
    desired for that field). The *titles* can be any :class:`string`
    or :class:`unicode` object and will add another entry to the
    fields dictionary keyed by the title and referencing the same
    field tuple which will contain the title as an additional tuple
    member.

    .. admonition:: Example

       Data type with fields ``r``, ``g``, ``b``, ``a``, each being
       a 8-bit unsigned integer:

       >>> dt = np.dtype({'names': ['r','g','b','a'],
       ...                'formats': [uint8, uint8, uint8, uint8]})

       Data type with fields ``r`` and ``b`` (with the given titles),
       both being 8-bit unsigned integers, the first at byte position
       0 from the start of the field and the second at position 2:

       >>> dt = np.dtype({'names': ['r','b'], 'formats': ['u1', 'u1'],
       ...                'offsets': [0, 2],
       ...                'titles': ['Red pixel', 'Blue pixel']})


``{'field1': ..., 'field2': ..., ...}``

    This style allows passing in the :attr:`fields <dtype.fields>`
    attribute of a data-type object.

    *obj* should contain string or unicode keys that refer to
    ``(data-type, offset)`` or ``(data-type, offset, title)`` tuples.

    .. admonition:: Example

       Data type containing field ``col1`` (10-character string at
       byte position 0), ``col2`` (32-bit float at byte position 10),
       and ``col3`` (integers at byte position 14):

       >>> dt = np.dtype({'col1': ('S10', 0), 'col2': (float32, 10), 'col3': (int, 14)})


:class:`dtype`
==============

Numpy data type descriptions are instances of the :class:`dtype` class.

Attributes
----------

The type of the data is described by the following :class:`dtype`  attributes:

.. autosummary::
   :toctree: generated/

   dtype.type
   dtype.kind
   dtype.char
   dtype.num
   dtype.str

Size of the data is in turn described by:

.. autosummary::
   :toctree: generated/

   dtype.name
   dtype.itemsize

Endianness of this data:

.. autosummary::
   :toctree: generated/

   dtype.byteorder

Information about sub-data-types in a :term:`record`:

.. autosummary::
   :toctree: generated/

   dtype.fields
   dtype.names

For data types that describe sub-arrays:

.. autosummary::
   :toctree: generated/

   dtype.subdtype
   dtype.shape

Attributes providing additional information:

.. autosummary::
   :toctree: generated/

   dtype.hasobject
   dtype.flags
   dtype.isbuiltin
   dtype.isnative
   dtype.descr
   dtype.alignment


Methods
-------

Data types have the following method for changing the byte order:

.. autosummary::
   :toctree: generated/

   dtype.newbyteorder

The following methods implement the pickle protocol:

.. autosummary::
   :toctree: generated/

   dtype.__reduce__
   dtype.__setstate__
